Question

Find the number of 4-digit positive integers divisible by either 3 or 7.

Answer 1

We need to find 4 digit numbers whose digits product is divisible by 3.
At least one of the digit is divisible by 3.
⇒ Required = Total − No digit is divisible by 3.
⇒ Total number of 4 digit numbers =9×10×10×10
=9000.
No digit is divisible by 3 →0,3,6,9 must not appear.
∴ Numbers should be formed using only 1,2,4,5,7,8=6 numbers.
⇒ No. of ways =6×6×6×6=6
4
=1296.
⇒ Required =9000−1296
=7704.
Hence, the answer is 7704.





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Answer 2

Step-by-step explanation:

We need to find 4 digit numbers whose digits product is divisible by 3.

At least one of the digit is divisible by 3.

⇒ Required = Total − No digit is divisible by 3.

⇒ Total number of 4 digit numbers =9×10×10×10

=9000

No digit is divisible by 3 →0,3,6,9 must not appear.

∴ Numbers should be formed using only 1,2,4,5,7,8=6 numbers.

No. of ways =6×6×6×6=6

4

=1296.

⇒ Required =9000−1296

=7704.

Hence, the answer is 7704.